Find the values of (Xx) that minimize the function f(x,y) = 8x²- xy + 12y² subject to the constraint x + y = 42. a. using the substitution method. b. using the Lagrange multiplier method.

Q: Problem 2. Forward elimination changes Ar =b to a row reduced Rx=d. Suppose that the complete…

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Q: Q1) Evaluate the integral S dy dx using polar coordinate

A: We have convert the given problem into polar coordinates.

Q: Q10: Following are the differential equations and their respective solutions. Select the incorrect…

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Q: The value of Ss (x + z) dy dz + (y + z) dx dz + (x + y) dx dy, Where 's' is the surface of sphere…

A: Here we can use divergence theorem to find the value of the given surface integral. Divergence…

Q: Find a 4x4 matrix A (NON-ZERO ENTRIES ONLY) with 3 eigenvectors coming from a single eigenvalue of…

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Q: Q1) Evaluate the integral dx dy using polar coordinate

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Q: Q3) Find the Area bounded by the curves y² = x and x = 2y - y?.

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Q: Let the characteristic equation of a 3 X 3 Matrix A be X3 + ad² + 47) – eigenvalue of A is 4 and a…

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Q: A coin is tossed three times. Let Hand T be the head and tail shown on the side of the coin facing…

A: We have to find (C union B')

Q: Q3. Tangents are drawn from 0(0,0) to the circle x² + y² – 2x + 4y+ 1 = 0, touching the circle at L…

A: The standard form of the equation of circle is   x-h2+(y-k)2=r2   where (h,k) is center of circle…

Q: 1. Draw the graph of the following relations and/or functions. Make sure that all "important" points…

A: Given are some functions in (a), (b) and (c)   To Graph the function, then find the domain, Range,…

Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin * +0) in…

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Q: If a ball is given a push so that it has an initial velocity of 24 ft/sec down a certain inclined…

A: Here we can use the fact that the velocity is the instantaneous rate of change of distance. That…

Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: X 1.7 1.8 1.9…

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Q: Q1) Evaluate the following integral using Partial Fractions Method: x3 + x2 dx x2 + x – 2

A: Indefinite integral

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) d²y z + 2y = 3 ,y…

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Q: Identify whether the following improper integral converges or diverges. If it converges, find its…

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Q: MTH315 Tutorial Activity 4 Subgroup of a Group Let G be a group, and let a,b be in G. Define the set…

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Q: Find the volume of the solid bounded by the planes z 0, 1%=1,1=2,y=-1,y-1 and the surface z=+.

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Q: Which of the following is the Taylor series expansion of the function f(x) =e-2 with center a 2n n!…

A: Given function is f(x) = e-x2

Q: у (0) %3D —2, у(0) ||

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Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9 2…

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Q: Q30. R = {(i, i), (i,n), (g, g), (n, n), (n, i), (o, i), (o, o), (0,n)} is a relation on set B =…

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Q: A number is drawn at random from the integers 20 to 40. Let A the event that the number is not less…

A: We have to solve the given problem.

Q: Consider the Solidas bound below by 3= N3(*2+y?), above by 2-1=N= -x?-y2 Its volume V (S); O The…

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Q: Q1) Evaluate the integral dx dy using polar coordinate

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Q: Q4) Find plane area inside polar function r 2 and outside polar function r= -2sine in third quarter.

A: We know the relation between polar and cartesian coordinates system, x = rcos(θ)   ,     y =…

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 5 6 Y 4 9 10 10 8 O3

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Q: Use the Lagrange multiplier method to optimize the objective function 3x? + y? – 2xy subject to the…

A: Given f(x) = 3x2 + y2 - 2xy Constraint: x + y = 6

Q: 2 -1 3 -1 3 If A = and B = 2 2 -1 find: ЗА - 2В A +2 (В — А) -5 (A + 2B)

A: Given matrices are A = 2-13012  and  B = -13-12-11

Q: Fine the 17th,19th and 21st terms of the Fibonacci sequence using this formula fn=fn-1+fn-2

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Q: By Gauss-lordan Method, solve the following system of linear equations. x+y+z+ w = 10 x- y+z-w = -2…

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Q: Find the length of the curve c(t) defined by c(t) = (-4 cos (t), –4 sin (t), t) if 0 < t< 2n and…

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Q: 2 -1 0 3 |, find 0 3 2 -1 1 2 If D = and E = DE

A: Matrix multiplication and operations

Q: Q4) Find plane area inside polar function r = 2 and outside polar function r = -2sine in third…

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Q: 3. (a) Show that the power series * does not converge uniformly for |2| < 1. k=1 (b) Show that the…

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Q: Problem: Chris left his home at past 3 o'clock PM as indicated in his wall clock. Between two to…

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Q: Three coins are tossed, what is the probability of the showing at least one tail? Your answer

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Q: | 10re", | 2:r3 + 3x² – 12x, r>0 * <0 Given: f(r) = (a) Identify all critical numbers of f. (b)…

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Q: Q3) Evaluate triple integral f, S, ya(x² – y²)dz dx dy.

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Q: o Find area inside r=2cos6 out Side

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Q: If two complex numbers are (*+) 21 5 + 5/3i) and z2 = + 2i 21 then radian value of the argument of…

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Q: Consider the solid bounded by the planes: z=x+y, z =12, x=0, y=0. Determine the volume of the solid.

A: Volume using the triple integral in rectangular coordinates is given by V=∬∫V dzdydx

Q: Find the arc length of the curve c(t) (2t, 19t|) for -1 <t < 1. (Express your answer as an exact…

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Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) + 2y = 3 , y (0) =…

A: Solution

Q: A bag contains x red paper clips, (x + 4) blue paper clips, and (3x – 11) white paper clips. A clip…

A: We have to find the value of x.

Q: Given 4x –9y =1. Find by implicit differentiation. dx

A: Given equation is 4x2 - 9y2 = 1

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

A: We have to find the volume of given bounded region.